Fixed Weight Aggregates Method
In fixed weight aggregates method, the weights used are neither from base period nor from current period but from a representative period. These weights are generally referred to as representative weights or as fixed weights. These fixed weights are unaffected by the selection of the base period. This is the advantage under this method. The user of the method will be able to select a base year that is convenient to him enabling him to change the price base yet retaining the fixed weights.
The students may refer to the weights assigned to various industry groups constituting the Index of Industrial Production presented in the annexure.
Fisher's Ideal method
Prof. Irving Fisher has proposed a formula for constructing index numbers, which is called the 'Fisher's Ideal Index'. The Ideal index is given by the following formula:
As evident from the above formula,
Fisher's Ideal Index is the geometric mean of the Laspeyres and Paasche indices.
The following advantages can be cited in favor of Fisher's Ideal Index:
Theoretically, geometric mean is considered the best average for the construction of index numbers and Fisher's index uses geometric mean.
As already noted, Laspeyres index and Paasche index indicate opposing characteristics and Fisher's index reduces their respective biases. In fact, Fisher's ideal index is free from any bias. This has been amply demonstrated by the time reversal and factor reversal tests.
Both the current year and base year prices and quantities are taken into account by this index.
Fisher's Ideal Index
The index is not widely used owing to the practical limitations of collecting data. Fisher's Ideal Quantity Index can be found out by the formula,